Question

Dacă x+(1/x)=5, atunci x²+(1/x²)=?

Answer 1

$x+\frac{1}{x}=5 |^2 \\\\\ (1+\frac{1}{x})^2=25 \\\\ x^2+2*x*\frac{1}{x}+\frac{1}{x^2}=25 \\\\ x^2+2+\frac{1}{x^2}=25 \ \ \ |(-2)\\\\ \boxed{x^2+\frac{1}{x^2}=23}$